Malleability of whole-number and fraction biases in decimal comparison.

Ren, Kexin; Gunderson, Elizabeth A.

doi:10.1037/dev0000797

Cited by 12 publications

(11 citation statements)

References 43 publications

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“…Among whole numbers, more digits always indicates a larger number, making it harder to determine the larger of 0.9 vs. 0.27 relative to pairs where the larger number also has more digits, such as 0.2 vs. 0.87. This string length congruity effect (Huber, Klein, Willmes, Nuerk, & Moeller, 2014) is found in children (Avgerinou & Tolmie, 2019;Ren & Gunderson, 2019) and adults (Varma & Karl, 2013) and even induces priming effects on subsequent processing in children and adolescents (Roell, Viarouge, Houde, & Borst, 2017. Other effects have also been investigated in decimal comparison (Huber et al, 2014;Varma & Karl, 2013), including the unit decade compatibility effect (slower reaction times when the tenths and hundredths digit conflicts, e.g., 0.19 vs. 0.86) and the zero facilitation effect (faster reaction for problems involving zero, see Appendix A).…”

Section: Role Of Inhibitory Control In Rational Number Understandingmentioning

confidence: 82%

“…Thus, abstracting a single index of fraction understanding from comparison tasks may be challenging without considering strategy information (Braithwaite, Pyke, & Siegler, 2017). Decimal comparison is not without strategy variation (Ren & Gunderson, 2019;Resnick et al, 1989). A further complication is that inconsistent decimals comparison involves interference from both numerical values of stimuli and also their physical length, as demonstrated by recent negative priming studies (Roell, Viarouge, Hilscher, Houde, & Borst, 2019;,.…”

Section: Decimal Comparison and Overall Math Skillsmentioning

confidence: 99%

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Linking inhibitory control to math achievement via comparison of conflicting decimal numbers

et al. 2021

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The relationship between executive functions (EF) and academic achievement is wellestablished, but leveraging this insight to improve educational outcomes remains elusive. Here, we propose a framework for relating the role of specific EF on specific precursor skills that support later academic learning. Starting from the premise that executive functions contribute to general math skills both directly -supporting the execution of problem solving strategies -and indirectly -supporting the acquisition of precursor mathematical content, we hypothesize that the contribution of domain-general EF capacities to precursor skills that support later learning can help explain relations between EF and overall math skills. We test this hypothesis by examining whether the contribution of inhibitory control on general math knowledge can be explained by inhibition's contribution to processing rational number pairs that conflict with individual's prior whole number knowledge. In 97 college students (79 female, age = 20.58 years), we collected three measures of EF: working memory (backwards spatial span), inhibition (color-word Stroop) and cognitive flexibility (task switching), and timed and untimed standardized measures of math achievement. Our target precursor skill was a decimals comparison task where correct responses were inconsistent with prior whole number knowledge (e.g., 0.27 vs. 0.9). Participants performed worse on these trials relative to the consistent decimals pairs (e.g., 0.2 vs. 0.87). Individual differences in the Stroop task predicted performance on inconsistent decimal comparisons, which in turn predicted general math achievement. With respect to relating inhibitory control to math achievement, Stroop performance was an independent predictor of achievement after accounting for age, working memory and cognitive flexibility, but decimal performance mediated this relationship. Finally, we found inconsistent decimals performance mediated the relationship of inhibition with rational number performance, but not other advanced mathematical concepts. These results pinpoint the specific contribution of inhibitory control to rational number understanding, and more broadly are consistent with the hypothesis that acquisition of foundational mathematical content can explain the relationships between executive functions and academic outcomes, making them promising targets for intervention.

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Section: Role Of Inhibitory Control In Rational Number Understandingmentioning

confidence: 82%

Section: Decimal Comparison and Overall Math Skillsmentioning

confidence: 99%

Linking inhibitory control to math achievement via comparison of conflicting decimal numbers

et al. 2021

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“…A robust phenomenon in studies on decimal comparison is lower accuracy and slower response times on comparisons that are incongruent with whole number knowledge (e.g., 0.9 vs. 0.23 because 23 > 9 but 0.23 < 0.9) (Avgerinou & Tolmie, 2020; Coulanges et al, 2021; Huber et al, 2014; Ren & Gunderson, 2019; Varma & Karl, 2013). Two explanations have been posited for this effect.…”

Section: Discussionmentioning

confidence: 99%

Adults systematically underestimate decimals and whole number exposure induces further magnitude-based underestimation.

Schiller¹,

Abreu-Mendoza²,

Rosenberg‐Lee³

2024

Journal of Experimental Psychology: Learning, Memory, and Cogni

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Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected stimuli to investigate how equivalent decimals (e.g., 0.8 and 0.80 on a 0-1 number line) and proportionally equivalent whole numbers (e.g., 80 on a 0-100 number line) are estimated. We find that young adults (n = 88, M age = 20.22 years, SD = 1.65, 57 female) have a linear response pattern for both decimals and whole numbers, but those double-digit decimals (e.g., 0.08, 0.82, 0.80) are systematically underestimated relative to proportionally equivalent whole numbers (e.g., 8, 82, 80). Moreover, decimal string length worsens the underestimation, such that single-digit decimals (e.g., 0.8) are perceived as smaller than their equivalent double-digit decimals (e.g., 0.80). Finally, we find that exposing participants to whole number stimuli before decimal stimuli induces magnitude-based underestimation, that is, greater underestimation for larger decimals. Together, these results suggest a small but persistent underestimation bias for decimals less than one, and further that decimal magnitude estimation is fragile and subject to greater underestimation when exposed to whole numbers.

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“…Similar priming phenomena were observed in tasks with symbolic formats. For example, Ren and Gunderson (2019) demonstrated that children primed with whole number comparison (or a flanker control task) prior to decimal comparison performed substantially worse on trials with incongruent rather than congruent whole number components (e.g., worse performance on .9 vs. .23 than .2 vs. .93). These differences between congruent and incongruent trials were not present when participants were primed with decimals (or fractions) before the decimal trials.…”

Section: Priming Effects In Rational Numbersmentioning

confidence: 99%

“…A limitation of the current work is that we do not have a non-numerical priming condition to act as a control for the priming effects. For example, Ren and Gunderson (2019) found that the non-numerical control priming condition (i.e., the flanker task) had similar effects to the whole number priming condition, namely, worse performance on a decimal comparison task relative to a fraction priming condition. This pattern of results suggests that among children, the default state is one where whole number knowledge interferes.…”

Section: Decimal Magnitude Representation Is Impacted By String Lengt...mentioning

confidence: 99%

Adults Systematically Underestimate Decimals and Whole Number Exposure Induces Further Magnitude-Based Underestimation

Schiller¹,

Abreu-Mendoza²,

Rosenberg‐Lee³

2022

Preprint

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Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be represented in infinite ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used carefully selected stimuli to investigate how equivalent decimals and whole numbers are represented on the number line. We find that young adults (N = 88, Mage = 20.22 Years, SD = 1.65, 57 female) have linear representations for both decimals and whole numbers, but that double-digit decimals (e.g., 0.08, 0.82, 0.80) are systematically underestimated relative to proportionally equivalent whole numbers (e.g., 8, 82, 80). Moreover, decimal string length worsens the underestimation, such that single-digit decimals (e.g., 0.8) are perceived as smaller than their equivalent double-digit decimals (e.g., 0.80). Finally, using a natural priming design, we find that presenting whole number stimuli before decimal stimuli induces magnitude-based underestimation, that is, greater underestimation for larger decimals. Together, these results suggest a small but persistent underestimation bias for decimals less than one, and further that decimal representation is fragile and subject to greater underestimation when exposed to whole numbers.

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Malleability of whole-number and fraction biases in decimal comparison.

Cited by 12 publications

References 43 publications

Linking inhibitory control to math achievement via comparison of conflicting decimal numbers

Linking inhibitory control to math achievement via comparison of conflicting decimal numbers

Adults systematically underestimate decimals and whole number exposure induces further magnitude-based underestimation.

Adults Systematically Underestimate Decimals and Whole Number Exposure Induces Further Magnitude-Based Underestimation

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